Answer:
The equation of the quadratic graph is f(x)= - (1/8) (x-3)^2 + 3 (second option)
Step-by-step explanation:
Focus: F=(3,1)=(xf, yf)→xf=3, yf=1
Directrix: y=5 (horizontal line), then the axis of the parabola is vertical, and the equation has the form:
f(x)=[1 / (4p)] (x-h)^2+k
where Vertex: V=(h,k)
The directix y=5 must intercept the axis of the parabola at the point (3,5), and the vertex is the midpoint between this point and the focus:
Vertex is the midpoint between (3,5) and (3,1):
h=(3+3)/2→h=6/2→h=3
k=(5+1)/2→k=6/2→k=3
Vertex: V=(h,k)→V=(3,3)
p=yf-k→p=1-3→p=-2
Replacing the values in the equation:
f(x)= [ 1 / (4(-2)) ] (x-3)^2 + 3
f(x)=[ 1 / (-8) ] (x-3)^2 + 3
f(x)= - (1/8) (x-3)^2 + 3
Ok so we know that y=1 so we can simply sub in the value of y into the equation :
y = -5x +3
1 = -5x +3
Move the -5x to the LHS ( Left-hand-side ) therefore it changes sign as well move 1 to the RHS ( Right-hand-side ) it also changes sign.
5x = 3 - 1
5x = 2
x = 2/5
x = 0.4
Hope this helps :).
When Anne Betty and Cynthia compared the amount of money each had, they discovered that Anne and Betty together had $12 Betty and Cynthia together had $18 and Anne and Cynthia together had $10.
<span>Who had the least amount of money? and how much was it?
a +b = 12
b + c = 18
a + c = 10
So what I did is simple XD A logical guess and check. I started with a = 1, but that was to little. And also didn't match up. So I kept going up and got a = 2, b = 10, and c = 8</span>
Answer:
The total cost of the party is approximately $2300, hence the correct answer is option D.
Step-by-step explanation:
Given:
Number of students = 295 students
cost per student = $8.95
Discounts given by the company = $400
To find:
We need to estimate the total cost of the party.
Solution:
To find the total cost of the party we need to multiply the total number of students into the cost per student.
This can be done as follows:
=295×8.95
=2640.25
Therefore, the total cost of the party is $2640.25, but it is given that the laser tag company gave the students a discount of $400. Hence the total cost after discount is
=2640.25-400
=2240.25
Therefore, the total cost of the party is approximately $2300
Hence the correct answer is option D.
Answer:
(3x - y)(3x + y)
Step-by-step explanation:
Both 9x^2 and y^2 are perfects squares.
The rule for factoring perfect squares is a^2 - b^2 = (a - b)(a + b).
Here, factoring (3x)^2 - y^2 results in (3x - y)(3x + y).
